Recognition of colors by photo-sensitive means

ABSTRACT

The invention refers to the method for the automatic recognition of coloring dyes, for instance in a drawing, by analysing in a number of primary colors or wave lengths the light reflected by the sample and by determining the position of the point representative of the responses of the photo-sensitive analysing means in a system of coordinates having a number of axes equal to the number of analysing wave lengths and wherein the permissible variations in the color attributes and density of each dye determine a locus which individualizes this dye. According to the invention, in order to facilitate discrimination between the dyes, the system of coordinates is changed and in the second system the loci are projected on one of the planes defined by each pair of axes of the said second system, their projections being separated by straight lines which are easily represented electronically. More generally, with a second system having n axes the loci may be projected on a figure having (n - 1) dimensions or less, this figure being preferably perpendicular to the n-sectrix of the first system of coordinates. Additionaly the loci may be divided into two groups by such a figure, electronic means determining on what side of the separating figure each representative point is situated.

United States Patent [191 Frappe Dec. 31, 1974 RECOGNITION OF COLORS BY [57] ABSTRACT PHOTO-SENSITIVE MEANS The invention refers to the method for the automatic recognition of coloring dyes, for instance in a drawing,

[75] Inventor: Plerre Frappe Lyon France by analysing in a number of primary colors or wave [73] Assignee: Verdol S.A., Caluire et Cuire, lengths the light reflected by the sample and by deter- France mining the position of the point representative of the [22] Filed: Nov. 6, 1973 responses of the photo-sensitive analysing means in a system of coordinates having a number of axes equal to the number of analysing wave lengths and wherein the permissible variations in the color attributes and density of each dye determine a locus which individu- Appl. No.: 413,371

P 'orit Data [30] F Z IE; Aplglcatlon n y 72 04392 alizes this dye. According to the invention, in order to e fame facilitate discrimination between the dyes, the system of coordinates is changed and in the second system [52] US. Cl 250/226, 8/25, 356/176 the loci are projected on one of the planes defined by [51] Int. Cl. G01 j 3/34 each pair of x f he said second system, their pro- [58] Field of Search 250/226; 356/173, 176, jections being separated by straight lines which are 356/175; 8/25 easily represented electronically. More generally, with a second system having n axes the loci may be pro- [56] References Cited jected on a figure having (n 1) dimensions or less,

UNITED STATES PATENTS this figure being preferably perpendicular to the nsectrix of the first system of coordinates. Additionaly 33%;???) iii??? iiii'fffiijii..........:::::::::::: 322/132 did iddi my id divided idid dwd giddpi iii dddi id Primary Examiner-James W. Lawrence Assistant Examiner-D. C. Nelms Attorney, Agent, or Firm-Dowell & Dowell ure, electronic means determining on what side of the separating figure each representative point is situated.

8 Claims, 12 Drawing Figures I X 52a! 51 a 51a 0 p r PATENTED HERB] I974 SHEET 2 BF 6 M 0 w I 2 r 5 I 2 T S L M H o m 1 m. S r M. a 2 .n .a ID 1 C e ,I //I 4 1 52 Al A w r I I I iw I X D 0 o I MW 1 I r C I My 1 ID 1/! m S2 m 4 1 I s S a Ix w o 4 4 n S PATENTED BEBBI I974 SHEET 5 OF 6 The present invention relates to the photo-electronic recognition of colors, or more exactly of coloring dyes, particularly for the reading-in of the designs used in the preparation of perforated cards or papers for loom jacquards.

In my prior US. Pat. No. 3,752,590 I have described a method which consists in determining the locus representative of each dye (taking into account the permissible variations in its color attributes and in its density on the sample being analysed) in a system of coordinates having an axis for each primary color (or wave length) selected for the analysing operation by means of photo-electric cells, in electronically representing geometrical figures which separate these loci from each other, and in determining between which of these figures the point representative of the responses of the cells for each spot of the sample is situated.

The procedure may frequently be simplified by considering the projections of the loci on the planes determined by the axes of the system of coordinates. The loci are then formed of plane figures corresponding to a pair of primary colors in each plane and the separating figures become straight lines (or successions of portion of straight lines). The electronic circuitry is thus greatly simplified. But it may occur that some loci overlap each other in all the planes though they are in fact separated from each other in the space which corresponds to the system of.coordinates.

It is an object of the present invention to avoid this disadvantage.

In accordance with this invention the system of coordinates is changed in the space and the loci are projected on the planes determined by the axes of the new system, the latter being selected in such manner that the projections of any pair of loci do not overlap each other in all the said planes.

The new system of coordinates may further be so se lected that one at least of the planes determined by its axes may form a separating figure between the loci. In other words this plane divides the loci into two groups respectively situated on one and the other side of the said plane and which may thus be differenciated from each other even if their projections overlap in that plane.

In the annexed drawings:

FIG. 1 shows the representative curve of a coloring dye versus the wave length of the reflected light.

FIG. 2 illustrates the loci of the colors of a design in the simplest case of two colors which may be satisfactorily analysed by means of only two wave lengths.

FIG. 3 shows how the two colors of FIG. 2 may be discriminated from each other by changing the system of coordinates.

FIG. 4 corresponds to a modification of FIG. 3.

FIG. 5 shows in the case of two colors how the space may be divided into two semi-spaces the loci thus being themselves divided into two groups.

FIG. 6 indicates how the locus of a color may be projected on a plane perpendicular to the trisectrix of the three coordinate axes in the case wherein the colors are analysed by means of three wave lengths.

FIG. 7 illustrates the projections thus obtained in the case of a design having seven colors.

FIG. 8 shows how a three-dimensional space may be divided into two semi-spaces by means of an appropriate plane in order that the loci of the colors may be themselves divided into two different groups.

FIG. 9 is a diagram illustrating how the coordinates of a new system may be electronically deduced from those of the former one.

FIG. 10 shows how a hyperplane in a fourdimensional space may be electronically represented.

FIG. 11 is a simplified diagram corresponding to the case wherein the hyperplane is perpendicular to the quadrisectrix of the coordinate axes.

FIG. 12 illustrates a more complicated diagram corresponding to a number of successive operations.

It is well known that any coloring dye may be analysed by being illuminated by a white light, the intensity of the light reflected being plotted versus its wave length. There is thus obtained a curve such as N (FIG. 1) which is representative of the dye. Since in actual practice the use of all the portions of such curves for the discrimination of the colors of a design or other support would lead to excessive complications the coloring dye is merely identified by the respective intensities y y y Ofa limited number of analysing wave lengths I A It The photo-sensitive devices (photo-electric cells and their circuitry) are further so arranged that ordinate corresponds to the white color of the support (this color being assumed to be perfect), the reflected intensities y y y then appearing in the form of percentages.

Considering for instance the discrimination of the colors in a design for the preparation of perforated paper bands for loom jacquards, the first step consists in determining the characteristics of each dye (or mixture of dyes) used in the design. The number of analysing wave lengths used should be as reduced as possible taking into account the similarities of the dyes. In order to simplify the explanations it will first be assumed that only two wave lengths are used, though this is quite exceptionally possible. v

FIG. 2 therefore illustrates two coordinate axes Ob-Or corresponding to two analysing wave lengths, respectively blue and red, these axes being graduated from zero to 100 in order to represent the intensities of the reflected light of the colored portions of the design as percentages of the white light reflected by the support thereof. With such an arrangement the center 0 corresponds to a black spot (no light reflected) and point M to a white spot (blue and red reflected equally to the maximum possible). In order to simplify the explanations it will be assumed that the design only comprises two colors C, and C If the coloring dyes used were perfect and if their density on the white paper or like support were sufficient and quite uniform, the responses of the photo-electric cells for all the spots of the drawing would be represented by one of the two points C and C But in actual practice the composition of a commercial dye varies within certain limits between successive batches and therefore for a given density the representative point may be situated within a curve 0 c more or less similar to a circle having its center respectively at C C A3 to the unavoidable variations in the density of application of the dye on the paper, it must be assumed that they remain between reasonable limits and under such conditions their effect is to extend the circle more or less towards M and O.

Finally the locus of each dye is a surface S,, S delimited by a more or less banana-shaped curve s1, s2.

It is obvious that in the quite simple case of FIG. 2, discrimination between the two colors is quite easy. It is sufficient to represent electronically the bissectrix OM. Any response of the photo-electric cells above OM corresponds to color C, while any response below OM corresponds to color C But in order to explain the characteristics of the present invention, it will be supposed that it is desired to use the method according to the said invention.

It will be remarked that if the loci 8,, S, are projected on axes Ob-Or, or on planes perpendicular to the plane of FIG. 2 and containing the said axes, the projection obtained overlap each other and are therefore exclusive of any discrimination.

In accordance with the invention this disadvantage is avoided by changing the system of coordinates. It is more particularly possible, as indicated in FIG. 3, to select for the new axes the bissectrix OM and a straight line X'OX perpendicular to the latter. It may easily be ascertained that the projections of S, and S, on the new axis X'X (or on a plane perpendicular to the plane of FIG. 3 and containing X'X) are formed of two segments sla-slb, s2a-s2b which are spaced from each other and are thus easily discriminated electronically. The projections s'la-slb, s2a-s2b on OM overlap each other, but this is of no importance since discrimination is obtained along axis X'X.

FIG. 4 illustrates a case wherein the loci 8,, S are such that they cannot be safely separated by the bissectrix OM. It is then generally possible to find another straight line AP which passes between the said loci. This line may be selected as one of the new axes of coordinates, the other X'OX being perpendicular to AP.

Here again the projections sla slb and s2a-s2b on axis X'OX are spaced from each other and may therefore be easily discriminated.

It will be noted that in FIGS. 3 and 4 axis X'X may remain spaced from the center of the initial coordinates.

It results from the above that a quite satisfactory means for the discrimination of the loci consists in projecting same on a plane X'X more or less perpendicular to the bissectrix OM of the axes of the initial system of coordinates bOr, this plane being obtained by changing the said system.

But it may also be noted that considering the plane perpendicular to the plane of the figure and which contains the axis O,P (FIG. 4) or OM (FIG. 3), it divides the space into two portions in which the loci S and S, are respectively situated. In the case of only two colors this remark is of no interest, but with a design comprising a large number of such colors their division into two separate groups reduces the risk that their projections overlap each other since each group is to be considered separately.

FIG. 5 shows for instance a case wherein owing to the number of colors of the design (two only of which are represented by loci 8,8,), the system of coordinates has been changed from bOr to XO,X-YO,Y, the loci being projected on axis X'OX. The projections sla-slb and s2a-s2b of loci S and S overlap each other, but they may be discriminated by the fact that the corresponding loci 8,, 8,, are respectively situated on one and the other side of a plane perpendicular to the plane of FIG. 5 and containing X'X.

The above developments are obviously of minor interest in the case of only two analysing wave lengths and with a quite limited number of colors. The representation only requires two axes of coordinates which determine a plane (the plane of FIG. 5, for instance) and it is easy to draw straight lines or segments of straight lines which separate the loci from each other in a manner which is easily transduced electronically. But generally the number of analysing wave lengths which must be used to individualize the coloring dyes is at least equal to three and often to four. Now a representation in a three-dimensional space is difficult while with four dimensions or more it is merely theoritical, and can only be dealt with by means of equations. It is then possible to proceed by considering the analysing wave lengths insuccessive pairs, as explained in my aforesaid US. Pat. No. 3,752,590. Considering a ndimensional space (with n 2) this procedure is tantamount to projecting the loci on the various planes determined by the n axes of coordinates, since each plane corresponds to two axes and therefore to two analysing wave lengths. But it may occur that in all these planes the projections of some loci overlap each other or are quite close to each other, whereby their discrimination is impossible or unsafe.

It is then of advantage to change the system of coordinates in such manner thatin one at least of the planes defined by the new axes the projections of the loci may be perfectly spaced from each other and easily separated by straight lines. It is more particularly possible to so select these new axes that one of the said planes be substantially perpendicular to the n-sectrix of the angle formed by the initial axes. Considering for instance the case of three analysing wave lengths, the loci of the coloring dyes must be represented in a threedimensional space with three axes Ob, 0], Or which may be illustrated in perspective as indicated in FIG. 6. The trisectrix is then the line OM which joins the black point 0 and the white point M. In order not to overcrowd the figure only one locus S, has been shown. X designates a plane perpendicular to OM; this plane may be considered as defined by two of the three axes of a new system of coordinates. The various loci 8,, S etc (only S, is illustrated in FIG. 6) are projected on that plane, as indicated at S, for locus S,. In FIG. 6 plane X contains point M but this is of course immaterial. FIG. 7 shows how the projections S, to S, of seven loci may appear in plane X as more or less regularly distributed around point M. It is generally easy to separate these projections by straight lines. If two projections overlapped in plane X the angle of the latter with respect to OM could be somewhat varied to obtain their separation provided this variation causes no overlapping of other loci.

The explanations given with reference to FIGS. 6 and 7 for the case of a three-dimensional space apply to four dimensions or more with this difference however that the system can no more by represented graphically and should be studied algebraically.

FIG. 8 shows how the loci may be divided into two groups by means of an appropriate plane in a threedimensional space. In many cases this plane X is substantially perpendicular to OM, as plane X of FIG. 6, but with this difference that its position along OM should be carefully selected. In such a case the loci are preferably projected on this separating plane X rather than on a different plane X. However the separating The coefficients a c characterize the new system. If in the latter the axes are perpendicular to each other, there coefficients follow the relations:

a a 17,12 6,0 O

(1 0 [7317 'l' C3C 0 These conditions may be represented electronically by means of three operational amplifiers 31, 32, 33 (FIG. 9), each having three inlets. The gains of these nine inlets are adjusted by means of resistances to analogically represent the nine coefficients a, 0

Thus when the analogs of the initial coordinates x, y, z are applied to the three inlets of each of these amplifiers, as illustrated, the outlets of same represent respectively the new coordinates u, v, w.

Considering now the case of a plane perpendicular to the n-sectrix and assuming that the system is fourdimensional (in order to demonstrate that the invention may be applied with more than three analysing wave lengths), this plane" is then a so-called hyperplane" having three dimensions. The problem remains as above, but with four coordinates (.r, y, z, t or u, v, w, r) instead of only three and with sixteen coefficients a (1 If the hyperplane is perpendicular to the quadrisectrix of the four axes of the four-dimensional system, then each of the three axes of this hyperplane is itself perpendicular to the said quadrisectrix. Assuming these three axes correspond to three of the four axes of the new system, then:

If these three axes are perpendicular to each other, then:

(1 0 [7217 CgCa l dgdg 0 (1 a, [73b l' C3C| l (1361 0 If now the fourth axis of the new system is parallel to the quadrisectrix of the initial system, the four coefficients a d are equal:

The new coordinates are given by the same equations as in the case of the three-dimensional space:

These equations, together with those between coefficients a (1,, have an illimited number of solutions. A particularly interesting one is:

the various coefficients a d, being equal either to l, or to zero. It is obviously quite easy to adjust the gains of four operational amplifiers, each with four inlets, to such simple values, inverters being used when necessary.

Concerning now the division of space by a plane, and taking here again the case of a theoritical fourdimensional space, the dividing plane is a hyperplane defined by an equation such as:

Such an equation may be represented by means of an operationalamplifier 34 (FIG. 10) having five inlets to receive the analogs x, y, z, I, E of the responses of the four analysing cells (one for each wave length), and of coefficient E itself. If properly adjusted this amplifier will yield an outlet-analogically equal to Ax By Cz 01+ 1 X E. If the spot being analyzed were in the hyperplane, the outlet value L would be zero. If the spot is on one side of this hyperplane L will be positive while if the spot is on the other side, L will be negative. In FIG. 10 reference 35 designates an inverter which permits of directly obtained E.

Of course if the system of coordinates have been changed the dividing hyperplane may be defined in the new system (coordinates u, v, w, r). If one of the axes of the new system is parallel to the quadrisectrix and if the dividing hyperplane is perpendicular to the letter, then its equation becomes:

r k (constant) In such a simplified case the hyperplane may be represented by an operational amplifier 36 (FIG. 11) having only two inlets to receive respectively r and k.

FIG. 12 illustrates by way of example the block diagram of an electronic discriminating apparatus for four analysing wave lengths (responses x, y, z, I of the four corresponding cells), wherein the coordinates are changed (new coordinates u, v, w, r), the projections of the loci being discriminated in the plane v-w by means of three separating straight lines A1, A2, A3, and with the four-dimensional space being divided by two hyperplanes P1, P2 perpendicular to the quadrisectrix. Operational amplifiers 37, 38, 39, 40 determine the new coordinates. Amplifiers 41 and 42 correspond to planes P1, P2, while the pairs 43, 44 and 45 represent straight lines Al, A2, A3. The outlets of the various devices are selectively applied to the five inlets of a number of AND gates such as 46, 47 each corresponding to the colors C 1, C2, etc. of the design (two only being shown in FIG. 12). The outlets of these gates individualize each of these colors.

it will be noted that the spot being analysed is of color Cl if it corresponds to a locus situated above Al and A2, but below Pl while for a spot of color C2 the locus should be below A1,. above A3, above P1 and below P2, the terms above and below only corresponding to the positive or negative character of the outlet of devices 41 to 45.

I claim:

l. A method for the automatic recognition of the coloring dyes used in a sample such as a drawing for the preparation of the perforated cards or bands for loom Jacquards, by means of photo-sensitive means which analyze in a number of wave lengths the light reflected by each of the dyes to be recognized when the corresponding portion of the sample is illuminated by a light beam of predetermined characteristics, recognition of each dye from which the light is reflected being based on the position of the point which represents the responses of the photo-sensitive means corresponding to each wave length in a first system of coordinates having n axes in which each of the n axes corresponds to one of said wave lengths, the response of each of said photo-sensitive means being plotted along the one of the axes of said first system which corresponds to the same wave length, said method including the following steps:

determining for each of said dyes to be recognized the permissible variations in its color attributes and in its density on the sample, in said first coordinate system;

determining in said first system of coordinates all the possible loci of points representative of the color attributes and density of each of said dyes to be recognized, taking into account said permissible variations, to thus obtain a number of loci equal to the number of said dyes;

transforming said first system of coordinates to obtain a second system having as many axes as said first system, each pair of axes of said second system defining a plane;

projecting said loci on at least one of said planes selected such that the projections of the loci do not intersect each other;

drawing in said one of said planes, lines which separate from each other the projections of said loci;

analogically representing each of said lines by electronic circuits having circuit means for each one of said planes equal to the number of separating lines, each of said circuits means receiving inlet signals corresponding to the coordinates of a point in said one of said planes and each emitting an outlet sig nal at a predetermined level when said last-named point is part of the separating line, at a level above said predetermined level when said last-named point is situated on one side of said last-named separating line, and at a level below said predetermined level when said last-named point is on the other side of said last-named separating line;

determining in said second system of coordinates the new coordinates of any representative point by transforming its coordinates in said first system as they result from the responses of said photosensitive means;

applying as said inlet signals to each of said electronic circuit means analog signals corresponding to the new coordinates of each representative point along the new axes which define said one of said planes;

and determining for each selected plane based upon the level of the outlet signals of said electronic circuit means which of said separating lines the projection of the representative point for each dye to be recognized is located between.

2. In a method as claimed in claim '1, the n axes of said first system of coordinates having a n sectrix and said one plane being substantially perpendicular to said n sectrix.

3. A method for the automatic recognition of the coloring dyes used in a sample such as a drawing for the preparation of the perforated cards or bands for loom Jacquards, by means of photo-sensitive means which analyze in a number of wave lengths the light reflected by each of the dyes to be recognized when the corresponding portion of the sample is illuminated by alight beam of predetermined characteristics, recognition of each dye from which the light is reflected being based on the position of the point which represents the responses of the photo-sensitive means corresponding to each wave length in a first system of coordinates having it axes in which each of the n axes corresponds to one of said wave lengths, the response of each of said photo-sensitive means being plotted along the one of the axes of said first system which corresponds to the same wave length, said method including the steps of:

determining for each of said dyes to be recognized the permissible variations in its color attributes and in its density on the sample, in said first coordinates system;

determining in said first system of coordinates all the possible loci of points representative of the color attributes and density of each of said dyes to be recognized, taking into account said permissible variations, to thus obtain a number of loci equal to the number of said dyes;

transforming said first system of coordinates to obtain a second system having n axes corresponding with the n axes of said first system;

selecting in said second system of coordinates a boundary figure having (n-l) dimensions and which separate said loci into two groups respectively situated on one and the other side of said figure;

analogically representing said separating figure by electronic circuit means having means for receiving inlet signals corresponding to the coordinates ofa point in said second system and in response to said inlet signals emitting an outlet signal at a predetermined level when said Iast-named point is part of said separating figure, at a level above said predetermined level when said last-named point is situated on one side of said separating figure, and at a level below said predetermined level when said last-named point is on the other side of said separating figure;

electronically determining in said second system of coordinates the new coordinates of any representative point by transforming its coordinates in said first system as they result from the responses of said photo-sensitive means;

applying as said inlet signals to each of said electronic circuit means analog signalscorresponding to the new coordinates of each representative point; and determining the level of the outlet signals of said electronic circuit means where with respect to said separating figure said last-named point is situated and therefore to which of said two groups of loci said last-named representative point corresponds.

4. In a method as claimed in claim 3, the step of projecting said loci on a plane defined by two of the n axes of said second system of coordinates, and distinguishing the projections which overlap each other in said plane by the fact that the loci to which they correspond are respectively situated in one and the other of said two groups.

5. In a method as claimed in claim 3, the step of projecting said loci on said separating figure and distinguishing the projections which overlap each other in said figure by the fact that the loci to which they correspond are respectively situated in one and the other of said two groups.

6. In a method as claimed in claim 3, said first system of coordinates having a n-sectrix and said separating figure being perpendicular to said n-sectrix.

7. In a method as claimed in claim 5, said first and second system of coordinates being tri-dimensional, each pair of their three axes defining a plane, and said separating figure being a separating plane parallel to one of the planes defined by a pair of axes of said second system.

8. In a method as claimed in claim 7, the three axes of said first system of coordinates having a trisectrix, and said second system being such that said separating plane is perpendicular to said trisectrix.

* l fl l 

1. A method for the automatic recognition of the coloring dyes used in a sample such as a drawing for the preparation of the perforated cards or bands for loom Jacquards, by means of photosensitive means which analyze in a number of wave lengths the light reflected by each of the dyes to be recognized when the corresponding portion of the sample is illuminated by a light beam of predetermined characteristics, recognition of each dye from which the light is reflected being based on the position of the point which represents the responses of the photo-sensitive means corresponding to each wave length in a first system of coordinates having n axes in which each of the n axes corresponds to one of said wave lengths, the response of each of said photoseNsitive means being plotted along the one of the axes of said first system which corresponds to the same wave length, said method including the following steps: determining for each of said dyes to be recognized the permissible variations in its color attributes and in its density on the sample, in said first coordinate system; determining in said first system of coordinates all the possible loci of points representative of the color attributes and density of each of said dyes to be recognized, taking into account said permissible variations, to thus obtain a number of loci equal to the number of said dyes; transforming said first system of coordinates to obtain a second system having as many axes as said first system, each pair of axes of said second system defining a plane; projecting said loci on at least one of said planes selected such that the projections of the loci do not intersect each other; drawing in said one of said planes, lines which separate from each other the projections of said loci; analogically representing each of said lines by electronic circuits having circuit means for each one of said planes equal to the number of separating lines, each of said circuits means receiving inlet signals corresponding to the coordinates of a point in said one of said planes and each emitting an outlet signal at a predetermined level when said last-named point is part of the separating line, at a level above said predetermined level when said last-named point is situated on one side of said last-named separating line, and at a level below said predetermined level when said last-named point is on the other side of said last-named separating line; determining in said second system of coordinates the new coordinates of any representative point by transforming its coordinates in said first system as they result from the responses of said photo-sensitive means; applying as said inlet signals to each of said electronic circuit means analog signals corresponding to the new coordinates of each representative point along the new axes which define said one of said planes; and determining for each selected plane based upon the level of the outlet signals of said electronic circuit means which of said separating lines the projection of the representative point for each dye to be recognized is located between.
 2. In a method as claimed in claim 1, the n axes of said first system of coordinates having a n sectrix and said one plane being substantially perpendicular to said n sectrix.
 3. A method for the automatic recognition of the coloring dyes used in a sample such as a drawing for the preparation of the perforated cards or bands for loom Jacquards, by means of photo-sensitive means which analyze in a number of wave lengths the light reflected by each of the dyes to be recognized when the corresponding portion of the sample is illuminated by a light beam of predetermined characteristics, recognition of each dye from which the light is reflected being based on the position of the point which represents the responses of the photo-sensitive means corresponding to each wave length in a first system of coordinates having n axes in which each of the n axes corresponds to one of said wave lengths, the response of each of said photo-sensitive means being plotted along the one of the axes of said first system which corresponds to the same wave length, said method including the steps of: determining for each of said dyes to be recognized the permissible variations in its color attributes and in its density on the sample, in said first coordinates system; determining in said first system of coordinates all the possible loci of points representative of the color attributes and density of each of said dyes to be recognized, taking into account said permissible variations, to thus obtain a number of loci equal to the number of said dyes; transforming said first system of coordinates to obtain a second system having n axes corresponding with the n axes of said first system; selecting in said second system of coordinates a boundary figure having (n-1) dimensions and which separate said loci into two groups respectively situated on one and the other side of said figure; analogically representing said separating figure by electronic circuit means having means for receiving inlet signals corresponding to the coordinates of a point in said second system and in response to said inlet signals emitting an outlet signal at a predetermined level when said last-named point is part of said separating figure, at a level above said predetermined level when said last-named point is situated on one side of said separating figure, and at a level below said predetermined level when said last-named point is on the other side of said separating figure; electronically determining in said second system of coordinates the new coordinates of any representative point by transforming its coordinates in said first system as they result from the responses of said photo-sensitive means; applying as said inlet signals to each of said electronic circuit means analog signals corresponding to the new coordinates of each representative point; and determining the level of the outlet signals of said electronic circuit means where with respect to said separating figure said last-named point is situated and therefore to which of said two groups of loci said last-named representative point corresponds.
 4. In a method as claimed in claim 3, the step of projecting said loci on a plane defined by two of the n axes of said second system of coordinates, and distinguishing the projections which overlap each other in said plane by the fact that the loci to which they correspond are respectively situated in one and the other of said two groups.
 5. In a method as claimed in claim 3, the step of projecting said loci on said separating figure and distinguishing the projections which overlap each other in said figure by the fact that the loci to which they correspond are respectively situated in one and the other of said two groups.
 6. In a method as claimed in claim 3, said first system of coordinates having a n-sectrix and said separating figure being perpendicular to said n-sectrix.
 7. In a method as claimed in claim 5, said first and second system of coordinates being tri-dimensional, each pair of their three axes defining a plane, and said separating figure being a separating plane parallel to one of the planes defined by a pair of axes of said second system.
 8. In a method as claimed in claim 7, the three axes of said first system of coordinates having a trisectrix, and said second system being such that said separating plane is perpendicular to said trisectrix. 